There are three types of fasteners that we're using on our car that I'd recommend purchasing ahead of time.
Bolts - most of the heavy devices should be bolted to the chassis. This includes such things as the fuse box, computer, ignition system, overflow tanks, etc. Depending on how the chassis is constructed, you may need short bolts to go through sheet metal or fiberglass, or longer bolts to go through chassis tubing. Many of these devices will require relatively small bolts (#6, #8, #10, and 1/4"). It's a good idea to have a selection of these bolts on hand. We also used bolts to attach wire and hose clamps where the fastener protruded into the cockpit. Two good places on the web to order bolts are Nutty and McMaster-Carr.
Sheet metal screws - stainless sheet metal screws are convenient to use for attaching wire and hose clamps, particularly if you want them to be removable. Keep in mind that you will probably end up adding or removing wires to your harness as your build progresses, so using removable fasteners for the wire clamps is a good idea. We are using primarily #6 and #8 screws of 1/2" to 5/8" inches. Sheet metal screws can be purchased from McMaster-Carr.
Pop rivets - these are an inexpensive and effective way to permanently attach things to the chassis if they are not going to be under a lot of stress. But keep in mind that they must be drilled out to be removed, so use them only when you're reasonably sure that the installation is permanent. We will probably end up replacing the sheet metal screws with pop rivets once we are satisfied that we won't be changing the wires. Another useful product if you are using pop rivets are Cleco Clamps. These are "temporary" rivets that are easily removed, but can be used when fitting panels, etc. They are available from Pegasus Racing as are rivets and tools.
Installation Tip - as you drill into the chassis, make sure you touch up the hole with Rustoleum or equivalent to prevent the exposed steel from rusting.